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GED Study GuideMATH
What you need to know about the GED Math Test®
1 You should be familiar with arithmetic and math concepts,
measurements, equations, andapplying math concepts to solve
real-life problems. Remember, the math test is not a memorization
test! You'll have access to a formula sheet thatgives you
information like how to calculate the area for different
shapes.
2 This study guide and the example questions in it will help you
get an idea of what’s going tobe on the test.3 You don’t need to
know everything in this guide! If you want to see how close you are
to passing, the GED Ready official practice test is a great
way to help you determine if you’re ready.®
Test Overview
Topics Basic Math Geometry Basic Algebra Graphs and
Functions
Time (to take the test) 115 minutes 3 minute break between parts
(to retrieve your calculator)
Format 2 parts Calculator allowed for part 2 Access to
calculator reference sheet and math formula sheet Multiple choice
and other question types (drag and drop, fill in the blank, hot
spot, anddrop down)
What you'll be tested on
The GED test will measure your strength in the skills below.
Click on a skill to learn more about it.
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Basic Math
1 Fractions and decimals in order
Place fractions and decimals in order.
For example, you can order the set of numbers:
in order from smallest to largest:
, 0.5, , 0.91
4
3
8
, , 0.5, 0.91
4
3
8
Example Questions
Fractions and decimals in order
Question:
Between which pair of decimals should be placed on a number
line?4
7
0.3 and 0.4A
0.4 and 0.5B
0.5 and 0.6C
0.6 and 0.7D
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2 Multiples and factors
Find multiples and factors.
For example:
the least common multiple of 3 and 5 is 15the greatest common
factor of 12 and 30 is 6
Example Questions
Multiples and factors
Question:Susan and Daphne are participating in a walk-a-thon at
the local community collegetrack to raise money. Susan can walk
around the track in 4 minutes. Daphne canwalk around the track in 6
minutes. Susan and Daphne started walking at the sametime. How many
minutes will it be until they complete a lap at the same time?
2A
10B
12C
24D
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3 Simplify exponents
Simplify numerical expressions with exponents
For example, 26 × 25 = 211
Example Questions
Simplify exponents
Question:Simplify.
`(2^9 × 3^5) × (2^4 × 3)^2`
`6^20`A
`6^24`B
`2^13 × 3^7`C
`2^17 × 3^7`D
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4 Distance between numbers on a number line
Find the distance between numbers on a number line using
absolute value.
For example, on a number line with points plotted at -2 and 4,
the distance between thepoints is 6.
Example Questions
Distance between numbers on a number line
Question:The points -4 and 5 are plotted on a number line. What
is the distance, in units,between the two points?
1A
4B
8C
9D
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5 Whole numbers, fractions, and decimal problems.
Compute and solve problems with whole numbers, fractions, and
decimals.
Example Questions
Whole numbers, fractions, and decimal problems.
Question:Simplify.
12 + 15 ÷ 3 × 6 – 4
18A
22B
38C
50D
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6 Squares, square roots, cubes, and cube roots
Calculate and compute with squares, square roots, cubes, and
cube roots of numbers.
Example Questions
Squares, square roots, cubes, and cube roots
Question:Add.
`3sqrt{7} + sqrt{7}`
`4sqrt{7}`A
`3sqrt{14}`B
`4sqrt{14}`C
`3sqrt{49}`D
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7 Undefined expressions
Know that expressions with a denominator of zero are "undefined"
and have no solution.
Identify "undefined" numerical expressions which have no
solution, including:
a denominator of zerosquare roots of negative numbers
Example Questions
Undefined expressions
Question:Which expression is undefined in the set of real
numbers?
`sqrt{-4}`A
`frac{0}{-4}`B
`0^4`C
`-4 × 0`D
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8 Unit rates
Find unit rates.
For example:
miles per hourdollars per pound
Example Questions
Unit rates
Each case contains 2 boxes of mineral water.Each box contains 4
bottles of mineral water.
A store charges $6.96 for a case of mineral water.
Question:What is the cost of each bottle of mineral water?
$0.87A
$1.16B
$1.74C
$3.48D
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9 Objects at scale
Use scale factors to convert dimensions between scale drawings
and actual objects.
For example, you might be presented with an image of the
dimensions of a room. Theimage may use 1 inch to represent 1 foot
of real space in the room.
Example Questions
Objects at scale
Question:A scale drawing of a house uses a scale of 0.5 inches =
2 feet. What is the length, ininches, of a line on the scale
drawing that represents an actual length of 5 feet?
1.25A
2.5B
10C
20D
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10 Multiple-step problems that use ratios, proportions,and
percents
Solve multiple-step problems that use ratios, proportions, and
percentages.
Examples of multi-step problems include:
Simple interestPercent increase and
decreaseGratuitiesCommissions
Example Questions
Multiple-step problems that use ratios, proportions, and
percents
Question:The price of Veronica’s meal before tax and tip was
$11.92. Veronica paid 8% tax,then added a 15% tip to the total. To
the nearest cent, how much did Veronica pay forher meal?
$12.87A
$13.71B
$14.66C
$14.80D
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11 QA
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Geometry
1 Side lengths of shapes when given the area orperimeter
Find the side lengths of triangles, rectangles, and polygons
when given the area orperimeter.
Remember, you will be provided with the math formulas.
Example Questions
Side lengths of shapes when given the area or perimenter
Question:A rectangle has an area of 54 square inches and a
length of 6 inches. What is thewidth, in inches, of the
rectangle?
9A
21B
24C
48D
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2 Area and perimeter of two-dimensional shapes
Find the area and perimeter of two-dimensional shapes, including
triangles, rectangles,polygons, and composite shapes.
Remember, you will be provided with the math formulas.
Example Questions
Area and perimeter of two-dimensional shapes
The Wilson family's back yard is a rectangular plot that has a
length of 100 feet and awidth of 80 feet. The family planted a
garden with a length and width of 60 feet. Thefamily planted a lawn
in the remaining area of the back yard, as shown.
Question:What is the area, in square feet, of the lawn in the
Wilson family's back yard?
4,400A
5,200B
5,600C
8,000D
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3 Area, circumference, radius, and diameter of a circle
Find the area and circumference of a circle. Find the radius or
diameter of a circle whengiven the area of circumference.
Remember, you will be provided with the math formulas.
Example Questions
Area, circumference, radius, and diameter of a circle
Greg installed a circular drain that has a diameter of 4.8
inches.
Question:To the nearest tenth of an inch, what is circumference
of the drain?
7.5A
15.1B
18.1C
30.1D
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4 Pythagorean theorem
Use the Pythagorean theorem to find a side length in a right
triangle.a2 + b2 = c2
Example Questions
Pythagorean theorem
The foundation of a building is in the shape of a rectangle,
with a length of 20 meters(m) and a width of 18 m.
Question:To the nearest meter, what is the distance from the top
left corner of the foundation tothe bottom right corner?
19A
27B
36C
38D
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5 Volume and surface area of three-dimensional shapes
Find the volume and surface area of three-dimensional shapes,
including rectangular andright prisms, cylinders, and right
pyramids. Find the side lengths, radius, or diameter of
athree-dimensional figure when given the volume or surface
area.
Remember, you will be provided with the math formulas.
Example Questions
Volume and surface area of three-dimensional shapes
A sphere has a radius of 7.5 centimeters (cm).
Question:To the nearest cubic centimeter, what is the volume of
the sphere?
236A
1,325B
1,766C
14,130D
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6 Graphical data including graphs, tables, and more
Construct and explain data from bar graphs, circle graphs, dot
plots, histograms, box plots,tables, scatter plots, and line
graphs.
Example Questions
Graphical data including graphs, tables, and more
The line graph shows the monthly payroll at a large construction
company.
Question:In which month did the monthly payroll decrease the
most?
FebruaryA
MarchB
JuneC
JulyD
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7 Mean, median, mode, and range
Find the mean, median, mode, and range of a number set. Find a
missing value whengiven an average.
Example Questions
Mean, median, mode, and range
The manager of an apartment complex ordered the air conditioners
in the apartmentsto be replaced. The list shows how many years each
air conditioner had been inservice.
12.2, 13.7, 11.9, 13.4, 11.9, 12.3, 12.9, 11.8, 13.3, 13.6
Question:What is the median number of years that an air
conditioner had been in service?
11.9A
12.1B
12.6C
12.7D
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8 Counting techniques
Use counting techniques to solve math problems. For example,
count how many differentways objects can be ordered, arranged, or
combined.
Example Questions
Counting techniques
Question:A restaurant serves custom-made omelets, where guests
select meat, cheese, andvegetables to be added to their omelet.
There are 6 vegetables available, and guestsmay select any 2
vegetables for their omelet. How many different combinations of
2vegetables are possible?
12A
15B
30C
36D
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9 Probability of an event
Find the probability of one or more events happening.
For example, what is the probability of drawing a jack or a king
randomly from a deck ofcards?
Example Questions
Probability of an event
Question:In a shipment of toys from a manufacturer, the
probability that a toy is defective is
. If Marie selects 2 toys from a shipment, what is the
probability that both toys are
defective?
1
50
A1
25
B1
50
C1
100
D1
2, 500
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Basic Algebra
1 Add, subtract, multiply, and factor linear expressions
Simplify linear expressions by adding, subtracting, multiplying,
expanding, and factoring.
For example:
Expand Factor
4(7x − 2)4x + 8
Example Questions
Add, subtract, multiply, and factor linear expressions
Question:Subtract.
(3x – 4y) – (4x – 3y)
A −x – y
B 7x – y
C −x – 7y
D 7x – 7y
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2 Evaluate algebraic expressions
Evaluate algebraic expressions by substituting (replacing)
variables with numbers.
Example Questions
Evaluate algebraic expressions
Question:A painter uses the expression to determine how much he
charges acustomer for a job that takes hours and cans of paint. His
last job required 3 cansof paint and took 15 hours to complete. How
much did the painter charge?
35h + 30ch c
$540A
$555B
$615C
$630D
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3 Algebraic expressions -- creation
Create algebraic expressions to represent problem situations or
word-to-symboltranslations.
Example Questions
Algebraic expressions -- creation
Question:In a science experiment, the initial temperature was 55
degrees Fahrenheit, andeach hour after, the temperature dropped by
4 degrees. Which expression representsthe temperature, in degrees
Fahrenheit, after hours?t
A 55 – 4t
B 55 + 4t
C 4t + 55
D 4t – 55
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4 Add, subtract, multiply, divide,and factor polynomials
Add, subtract, multiply, divide, and factor polynomials.
For example:
Factor (x + 8)(x + 4)
3x2 − 10x − 8
Example Questions
Add, subtract, multiply, divide,and factor polynomials
Question:Multiply.
(2x– y)(3x + y)
A 6x2 – xy – y2
B 5x2 – xy – y2
C 6x2 – xy – 2y2
D 5x2 – xy – 2y2
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5 Create polynomials from written descriptions
Create polynomials to represent problem situations or
word-to-symbol translations.
For example, a triangle has three sides with the following
lengths:
units, units, and units
Write an algebraic expression for the perimeter of the triangle
in units.
2x + 1 3x + 5 4x − 1
Example Questions
Create polynomials from written descriptions
Question:A rental company carries tables that seat 2, 4, or 8
people. For a wedding, acustomer orders tables that seat 2 people,
tables that seat 4 people, and tablesthat seat 8 people. Which
expression represents the number of people who could beseated at
the tables that the customer orders?
x y z
A 2x(4y)(8z)
B 2x + 4y + 8z
C (2 + 4 + 8)(xyz)
D (2 + 4 + 8)(x + y + z)
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6 Add, subtract, multiply and divide rational expressions
Add, subtract, multiply and divide rational expressions.
Example Questions
Add, subtract, multiply and divide rational expressions
Question:Add.
+3
x
x
x + 2
A3 + x
2x + 2
Bx + 5
2x + 2
Cx2 + 3x + 2
x(x + 2)
Dx2 + 3x + 6
x(x + 2)
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7 Write an expression from a written description
Write an expression from a written description.
Example Questions
Write an expression from a written description
Question:
A written description of a mathematical expression is shown.
the quotient of the sum of 4 and 2 times a number, and the
difference of 6 lessthan 3 times the same number
Which expression matches the written description?
A2x + 4
3x − 6
B2x + 4
6 − 3x
C (2x + 4)(3x – 6)
D (2x + 4)(6 – 3x)
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8 Use linear equations to solve real-world problems
Use linear equations to solve real-world problems. For example,
calculate the fuelefficiency of a car at different speeds.
Example Questions
Use linear equations to solve real-world problems
Question:Lucy is shipping 5 boxes that all weigh the same, and 1
envelope that weighs 7.5pounds. The total weight of the shipment is
65 pounds. What is the weight, inpounds, of each box?
5.5A
11.5B
14.5C
20.5D
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9 Solve a system of two linear equations
Solve a system of linear equations and real-world problems that
involve them.
Common techniques include graphing, substitution, or addition to
compute a system of twolinear equations.
Example Questions
Solve a system of two linear equations
Question:
A system of equations is shown.
4x + 3y = 84x – 3y = −16
What is the value of ?x
-3A
-1B
1C
4D
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10 Solve inequalities and graph the answer on a numberline
Solve inequalities and real-world problems that involve them,
and graph the solutions.
Example Questions
Solve inequalities and graph the answer on a number line
Question:Isabella saved $15,000 and bought a car that cost
$12,700. The insurance for the carwill cost $600 per year. How many
full years will Isabella be able to pay for carinsurance with her
remaining savings?
3A
4B
21C
25D
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11 Quadratic equations with one variable
Solve quadratic equations with one variable.
For example, .3x2 + 2x − 8 = 0
Example Questions
Quadratic equations with one variable
Question:Solve.
4x2 – x – 5 = 0
and A x = −1 x =5
4
and B x =4
5x = 1
and C x = −1 x =4
5
and D x = 1 x =5
4
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Graphs and Functions
1 Locate points and graph equations
Locate points and graph linear equations in a coordinate
plane.
Example Questions
Locate points and graph equations
Points J, K, and L are plotted on a coordinate grid.
Question:What are the coordinates of the points on the
coordinate grid?
J (1, -4); K (3, 0); L (-2, 3)A
J (-4, 1); K (0, 3); L (3, -2)B
J (-4, 1); K (0, 3); L (-2, 3)C
J (-4, 1); K (3, 0); L (3, -2)D
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2 Slope of a line from a graph, equation, or table
Find the slope of a line from a graph, equation, or table.
Example Questions
Slope of a line from a graph, equation, or table
Question:What is the slope of the line represented by the
equation ?3x + 4y = 8
A −4
3
B −3
4
C3
4
D4
3
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3 Proportional relationships for equations and graphs
Determine whether an equation and a graph show the same
proportional relationship.
Example Questions
Proportional relationships for equations and graphs
Question:Chelsea designs beaded bracelets. The equation can be
used tofind the price, , of a bracelet that has beads. What does
the number in theequation represent?
P = 7 + 0.05bP b 0.05
the price of each beadA
the price of each braceletB
the number of bracelets madeC
the number of beads in a braceletD
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4 Features of graphs and tables for linear and
nonlinearrelationships
Identify features of graphs and tables for linear and nonlinear
relationships.
For example, using the rise/run to determine slope, coordinates
of points, and x/y intercept.
Example Questions
Features of graphs and tables for linear and nonlinear
relationships
Question:Kirsten walks up 6 flights of stairs to her office each
morning as part of her exerciseroutine. She walks the first 3
flights, rests for 30 seconds, walks the next 2 flights atthe same
rate of speed as she walked the first 3 flights, rests again for 30
seconds,and then walks the last flight of stairs at the same rate.
Which graph representsKirsten walking up the stairs?
A B
C D
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5 Slope and a point on a line
Find the equation of a line when given the slope and a point on
the line.
Example Questions
Slope and a point on a line
Question:What is the equation of the line that has a slope of -7
and passes through the point(4, 8)?
A x + 7y = 60
B 7x + y = 36
C x – 7y = −52
D 7x – y = 20
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6 Equation of a line from two points
Find the equation of a line from two points on the line.
Example Questions
Equation of a line from two points
Question:What is the equation of the line that passes through
the points (-3, -2) and (1, 6)?
A y = 2x + 4
B y = − 2x + 8
C y = x −1
2
1
2
D y = x −1
2
11
2
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7 Use slope of a line
Use the slope of a line to solve problems, for example identify
whether lines are parallel orperpendicular.
Example Questions
Use slope of a line
Question:What is the slope of a line that is perpendicular to
?5x – 2y = 1
A−5
2
B−2
5
C2
5
D5
2
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8 Functions shown in different ways
Compare functions that are shown in different ways, such as
tables, graphs, equations andwritten descriptions.
Example Questions
Functions shown in different ways
Question:Tim is looking at two websites that allow customers to
print their own designs on T-shirts. One website charges $24 per
T-shirt plus $8 shipping. The other website usesthe equation to
find the total cost, , of printing T-shirts. What isthe difference
in the cost of each website if Tim orders 10 T-shirts?
C = 22n + 12 C n
$2A
$16B
$20C
$24D
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9 Functions in tables and graphs
Recognize a function in a table or graph by determining whether
or not there is only oneoutput value for each input value.
Example Questions
Functions in tables and graphs
Question:Which table represents a function?
A B
C D
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10 Evaluating functions
Evaluate a function.
For example:
; find f(x) = x2 − 3x f( − 8)
Example Questions
Evaluating functions
Question:What is the value of f(x) = 3x2 + 4 when x = - 3?
-77A
-23B
31C
85D
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